A cylinder shaped can needs to be constructed to hold 550 cubic centimeters of soup. The material for the sides of the can costs 0.04 cents per square centimeter. The material for the top and bottom of the can need to be thicker, and costs 0.08 cents per square centimeter. Find the dimensions for the can that will minimize production cost. Helpful information: h: height of can, r : radius of can Volume of a cylinder: V = ar²h Area of the sides: A = 2rrh Area of the top/bottom: A To minimize the cost of the can: Radius of the can: Height of the can: Minimum cost: cents
A cylinder shaped can needs to be constructed to hold 550 cubic centimeters of soup. The material for the sides of the can costs 0.04 cents per square centimeter. The material for the top and bottom of the can need to be thicker, and costs 0.08 cents per square centimeter. Find the dimensions for the can that will minimize production cost. Helpful information: h: height of can, r : radius of can Volume of a cylinder: V = ar²h Area of the sides: A = 2rrh Area of the top/bottom: A To minimize the cost of the can: Radius of the can: Height of the can: Minimum cost: cents
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Transcribed Image Text:A cylinder shaped can needs to be constructed to hold 550 cubic centimeters of soup. The material for the
sides of the can costs 0.04 cents per square centimeter. The material for the top and bottom of the can
need to be thicker, and costs 0.08 cents per square centimeter. Find the dimensions for the can that will
minimize production cost.
Helpful information:
h: height of can, r: radius of can
Volume of a cylinder: V = Tr²h
Area of the sides: A = 2arh
Area of the top/bottom: A
= TI
To minimize the cost of the can:
Radius of the can:
Height of the can:
Minimum cost:
cents
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Step 1: Given
VIEWStep 2: Let the variables and determine the cost function
VIEWStep 3: Determine the cost function in terms of r only
VIEWStep 4: Find the critical point that minimizes the production cost
VIEWStep 5: Check the production cost is minimum at the critical point using second derivative test
VIEWStep 6: Determine the radius, height and minimum cost of the can
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